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Pseudocharacters on free semigroups invariant with respect to their automorphism groups


Author: V. A. Faiziev
Journal: Proc. Amer. Math. Soc. 126 (1998), 333-342
MSC (1991): Primary 20M15, 20M30
DOI: https://doi.org/10.1090/S0002-9939-98-04110-0
MathSciNet review: 1422867
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Abstract: Let $\mathcal{F}$ be a free semigroup and let $A$ be an automorphism group of $\mathcal{F}$. A description is given of the space of real functions $\varphi $ on semigroup $\mathcal{F}$ satisfying the following conditions:

1) the set $\{\varphi (xy)-\varphi (x)-\varphi (y);\,\, x,y\in \mathcal{F} \}$ is bounded;

2) $\varphi (x^{n}) = n\varphi (x)$ for any $x\in \mathcal{F}$ and $n\in N$;

3) $\varphi (x^{\tau }) = \varphi (x) \quad \forall x\in \mathcal{F}$, and $\forall \tau \in A$.


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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-98-04110-0
Keywords: Semigroup, free semigroup, group, semidirect product, function, endomorphism, automorphism, pseudocharacter, character, linear space
Received by editor(s): December 19, 1995
Received by editor(s) in revised form: June 26, 1996, and July 26, 1996
Communicated by: Palle E. T. Jorgensen
Article copyright: © Copyright 1998 American Mathematical Society

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